12-d-6d^2=9

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Solution for 12-d-6d^2=9 equation:


Simplifying
12 + -1d + -6d2 = 9

Solving
12 + -1d + -6d2 = 9

Solving for variable 'd'.

Reorder the terms:
12 + -9 + -1d + -6d2 = 9 + -9

Combine like terms: 12 + -9 = 3
3 + -1d + -6d2 = 9 + -9

Combine like terms: 9 + -9 = 0
3 + -1d + -6d2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-0.5 + 0.1666666667d + d2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.1666666667d + 0.5 + d2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.1666666667d + d2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.1666666667d + d2 = 0 + 0.5
0.1666666667d + d2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.1666666667d + d2 = 0.5

The d term is 0.1666666667d.  Take half its coefficient (0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
0.1666666667d + 0.006944444447 + d2 = 0.5 + 0.006944444447

Reorder the terms:
0.006944444447 + 0.1666666667d + d2 = 0.5 + 0.006944444447

Combine like terms: 0.5 + 0.006944444447 = 0.506944444447
0.006944444447 + 0.1666666667d + d2 = 0.506944444447

Factor a perfect square on the left side:
(d + 0.08333333335)(d + 0.08333333335) = 0.506944444447

Calculate the square root of the right side: 0.712000312

Break this problem into two subproblems by setting 
(d + 0.08333333335) equal to 0.712000312 and -0.712000312.

Subproblem 1

d + 0.08333333335 = 0.712000312 Simplifying d + 0.08333333335 = 0.712000312 Reorder the terms: 0.08333333335 + d = 0.712000312 Solving 0.08333333335 + d = 0.712000312 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + d = 0.712000312 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + d = 0.712000312 + -0.08333333335 d = 0.712000312 + -0.08333333335 Combine like terms: 0.712000312 + -0.08333333335 = 0.62866697865 d = 0.62866697865 Simplifying d = 0.62866697865

Subproblem 2

d + 0.08333333335 = -0.712000312 Simplifying d + 0.08333333335 = -0.712000312 Reorder the terms: 0.08333333335 + d = -0.712000312 Solving 0.08333333335 + d = -0.712000312 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + d = -0.712000312 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + d = -0.712000312 + -0.08333333335 d = -0.712000312 + -0.08333333335 Combine like terms: -0.712000312 + -0.08333333335 = -0.79533364535 d = -0.79533364535 Simplifying d = -0.79533364535

Solution

The solution to the problem is based on the solutions from the subproblems. d = {0.62866697865, -0.79533364535}

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